A few years ago, I had a PowerBook Duo 280 that behaved just like this. I did a lot of looking on archived discussion boards, and asking around here, for a cure at the time.
As I recall, what I came up with was that the earliest active matrix greyscale LCDs found on the PowerBook 170 (I think), and certainly the 180, 270, and 280 (all the ones that have a "glassy" surface) are all prone to this, and that there is no known repair. But not all of them have the defect, so the fix is to find a working replacement LCD: my 180, for example, is absolutely fine, whereas my 280 still awaits a donor....
It is not a failure of the backlighting, but is apparently the result of a failure in the "edges" of the LCD itself. It is not merely a VRAM problem either, as in my 280, I went to the trouble of replacing the logic board with a known-good one from a working 280c: no joy, as the same problem resulted.
If you find out differently, do let us all know!